Effects of the infinitely fast and infinitely slow A <b>+</b> B <b>→</b> C reaction on the miscible viscous fingering: Theoretical and numerical analyses

The effect of irreversible A+B → C reaction on viscous fingering (VF) instability was studied through theoretical and numerical methods. Using newly defined log-viscosity ratios, RPhys and RChem in our previous study [M. C. Kim et al., “Unstable miscible displacements in radial flow with chemical reactions,” J. Fluid Mech. 917, A25 (2021)], linear stability equations were derived on the reactive systems whose viscosity distribution and the stability characteristics are systematically classified according to RPhys and RChem. Linear stability analysis identified the least stable initial disturbances, which have a large negative growth rate, meaning that the system is unconditionally stable at the very initial stage, regardless of the values of RPhys and RChem. Over the extended time period, stability analysis was conducted using the quasi-steady state approximation in the self-similar domain. Adopting the linear stability analysis results as an initial condition for nonlinear numerical simulations, the development of VF was successfully demonstrated, finding that chemical reactions induce the VF instability even for the physically stable (RPhys&amp;lt;0) and neutral (RPhys=0) systems, and accelerate and retard the growth of VF for physically unstable systems (RPhys&amp;gt;0). Furthermore, it was clarified that the infinitely fast reaction system degenerates into the nonreactive one, if RChem=0, which was a limitation that could not be explained in previous studies.